When an earthquake or large meteor strikes the earth or moon, it can ring like a bell for a long time, as shock waves bounce to and fro, slowly dying out. That can happen in culture too: some events are like earthquakes that shake a formerly stable landscape. Stravinsky’s Rite of Spring is one of those cultural earthquakes. There was a riot at its début in Paris in 1913.

Ferenc Puskás (1927-2006) (pronounced roughly FEHR-ents PUSH-kaash) was the orchestrator of another Slavic earthquake, forty years later and about 150 miles north-west, in London. Except that Puskás wasn’t Slavic and didn’t speak a Slavic language. Hungarians and their language aren’t Eastern European in any conventional sense. Instead, they invaded Eastern Europe and overturned a Slavic tradition. Puskás and his Magyar team-mates invaded and overturned another tradition when they beat England 3-6 at Wembley Stadium in November 1953.

How could that happen? As György Szöllősi says viâ his translators Andrew Clark and Matthew Watson-Broughton, it was generally accepted at the time that “England were invincible on their own turf” (“The Magical Magyars”, pg. 60). At the return match in Budapest in May 1954 Hungary did it again. Only more so: this time the score was 7-1. Tom Finney, himself one of the all-time greats, said that it was like “cart horses playing race-horses” (pg. 61). Puskás scored twice in both games and one of those goals, created by a pull-back that sent Billy Wright sliding off the pitch at Wembley, is one of the most famous of all time.

If his career had ended after he came off the pitch in Budapest, Puskás would have sealed his place in footballing history. And it did soon look as though his career might be over. Stalin died in 1953 and increasing unrest in Hungary led to full rebellion in 1956. Bullet-holes in the parliament buildings in Budapest still show what happened next: the rebellion was brutally crushed. Puskás was one of more than 200,000 Hungarians who went into exile.

He wasn’t able to return for decades and his fellow countrymen could only whisper about the remarkable feats he performed when he managed to find a new club. It was called Real Madrid and Puskás joined Alfredo Di Stéfano to become one of its greatest ever players: he scored seven goals in two European Cup Finals for the club. His first batch was four, in the 7-3 crushing of Eintracht Frankfurt in Glasgow in 1960. Then he scored a hat-trick against Benfica in 1962.

Unfortunately, Benfica scored five goals and no-one else scored for Real. Even the greats don’t always win, but that hat-trick proves that Puskás could do remarkable things even in defeat. His statistics are astonishing, reminiscent of Don Bradman’s in cricket: 511 goals in 533 Hungarian and Spanish top-flight games and 84 goals in 85 games for Hungary. The former Manchester United manager Alex Ferguson is one of those who are still awed by Puskás: Ferguson writes the foreword to this book and says he “dodged school” in 1953 to watch Hungary play England at Wembley. FIFA now have a Puskás award for goal of the year and there’s a photo of Cristiano Ronaldo holding up a red number 10 shirt bearing the name Puskás.

Ronaldo is another great, but his challenges off the pitch are remembering where he left the keys for his Lamborghini and deciding which ear to put his diamond stud in. Puskás lived through the Second World War, then saw a team-mate, Sándor Szůcs, hanged for trying to leave Hungary, then came under sentence of death himself when he went into exile after the Hungarian Uprising. He didn’t wear diamonds, he was a diamond in the Aranycsapat, the Golden Team that was the pride of Hungary before Puskás and team-mates like Zoltán Czibor and Sándor Kocsis became unpersons as traitors to the communist state.

This biography is short and easy to read, but it would have been improved by an index and contents page. Puskás’s career would have been improved by a World Cup winner’s medal and György Szöllősi describes why he didn’t get one. He also describes what Puskás’s real ancestry was and why he censored his birthdate. Hungary is an interesting country in lots of ways and it’s still making more of a mark in Europe than its size and population might lead you to expect. Puskás put his mark on European history in ninety minutes at Wembley in 1953, but he did much more than that and this book tells you how.

A fascinating book in a number of ways. First the obvious way: probability contains some of the strangest and most counter-intuitive mathematics that amateurs can easily understand. I could cope with a lot of this book, but it still stretched and even re-shaped my mind and my understanding of the world more deeply than almost any art has. There are very odd things to be found even in something as simple as the patterns of heads-and-tails in coin-tossing. For example, although HH and HT are equally likely to occur first when you start tossing a fair coin, “more tosses are necessary, on average, for HH than for HT to turn up”. That just doesn’t make sense at first glance. It’s a paradox, in other words, and if you can understand it you’ve taken a step even the most intelligent human beings were once unable to take.

Much less subtle, but probably much more important in life, is this:

Consider two random events with probabilities of 99% and 99.99%, respectively. One could say that the two probabilities are nearly the same, both events are almost sure to occur. Nevertheless the difference may become significant in certain cases. Consider, for instance, independent events which may occur on any day of the year with probability p = 99%; then the probability that it will occur every day of year is less than P = 3%, while if p = 99.99%, then P = 97%. (ch. 1, “Classical paradoxes of probability theory”, pp. 54-5)

Then there’s the question of why buses always seem to run “more frequently in the opposite direction”. The mathematics gets much trickier here, but that’s an example of how maths, unlike so much of the modern humanities, can extract deep meaning from apparently simple things because deep meaning is actually there. Mathematics is both the most fundamental and the purest of all subjects, and is something that can unite minds across barriers of language, culture, and politics.

This book is a good example of that, because it was first published not only in a communist country but in what is, to most Europeans, a very strange language: Hungarian. Hungarian isn’t part of the Indo-European family spoken almost everywhere else. If this book had been written in French or German or Spanish, its original title would look more or less familiar to an English-speaker. But its original title in Hungarian ― Paradoxonok a véletlen matematikában ― looks very odd. Even without being told, you could guess from some of the English that the book is a translation, but that adds to its charm and helps prove the universality of mathematics. A Hungarian can speak mathematics to anyone without an accent, and vice versa ― though I suspect that the mathematics here occasionally stutters because of typos. The English certainly does, but then the book was printed under communism, which did not encourage efficiency and attention to detail. Communism is gone now, Hungarian and maths both continue, but maths will outlast Hungarian, just as it will outlast all other languages spoken today.Vivat regina!